Use the hypothetical pair
Unless the question changes an assumption, weights are 40/60, standard deviations 20%/10%, and correlation 0.3. Every quantity uses one common return period. The questions are original teaching tasks, not official exam items.
Identify the requested output
State whether the task asks for covariance, variance, standard deviation or a comparison. A correctly calculated number with the wrong unit does not answer the same question. Review the corresponding worked example after an error.
Try the questions
What is Cov(A,B) in decimal-return units?
- A.
0.006
- B.
0.3
- C.
0.06
Answer and explanation
Answer: A
Multiply correlation by both compatible standard deviations.
- A
0.3×0.2×0.1 converts correlation to covariance.
- B
This is the correlation itself.
- C
This is ten times the covariance product.
What is the total portfolio variance in decimal-return units?
- A.
0.01
- B.
0.01288
- C.
0.14
Answer and explanation
Answer: B
0.0064+0.0036+0.00288=0.01288.
- A
This drops the cross term.
- B
The own terms and both covariance products are included.
- C
This is weighted standalone dispersion, not variance.
Portfolio dispersion is about 11.349%. Which comparison follows?
- A.
It is lower than every individual asset
- B.
It is below the weighted 14% comparator but above B’s 10%
- C.
It guarantees a better investment
Answer and explanation
Answer: B
Name the baseline before interpreting a diversification reduction.
- A
Asset B’s dispersion is 10%, below this result.
- B
Both baselines are explicitly identified.
- C
Returns, suitability and other risks are not supplied.